This paper aims to propose an iterative mathematical morphology (IMM) filter methodology to de-noise the acoustic emission (AE) signal with impulsive noise. To develop the principle of IMM filter, a simulation signal is used to be de-noised by the conventional MM filter. Moreover, a novel approach is introduced to eliminate the end effect of MM filter by connecting the initial point with the end point of the time series. Therefore, the IMM filter can be realized based on the operations of MM filter and the elimination method of end effect. The noise elimination of a simulation signal indicates that the IMM filter can remove the impulsive noise more effectively than the MM filter and maintain useful information as much as possible. Two AE signals acquired from rock compression experiment, which are polluted by electromagnetic impulsive noise, are de-noised by the IMM filter, the conventional digital filter and the wavelet filter respectively. Compared with the other two methods, the IMM filter can preserve the essential information contained in AE signal better, especially the arrival time. These two experiments manifest the effectiveness of the IMM filter in de-noising issues of AE signals polluted by impulsive noise